Thermal Systems and Performance Evaluation

Introduction and Context

Thermal systems convert, transfer, or control energy. In mechanical engineering laboratories, their performance cannot be judged from theory alone: measured temperatures, pressures, flow rates, electrical inputs, fuel consumption, and emissions must be combined through energy balances and suitable performance indicators. This chapter develops experimental methods for internal-combustion engines, boilers, compressors, refrigeration and air-conditioning systems, and heat exchangers.

The first law of thermodynamics provides the central accounting principle. For a control volume operating at steady state,

where Q̇ is heat transfer to the system (W), Ẇ is work delivered by the system (W), ṁ is mass flow rate (kg/s), and h is specific enthalpy (J/kg). Changes in kinetic and potential energy are often negligible in laboratory equipment, but this assumption must be checked rather than applied automatically.

Learning Objectives

After completing this chapter, a student should be able to:

1. plan and conduct performance tests on major thermal systems;
2. identify instruments, calibration requirements, and experimental uncertainties;
3. calculate brake power, efficiencies, heat balances, coefficient of performance, and heat-exchanger effectiveness;
4. interpret performance changes with load, pressure ratio, temperature, and flow rate;
5. evaluate emissions and identify practical sources of error;
6. prepare a technically defensible laboratory report and recommend improvements.

Experimental Method: From Measurement to Performance

A reliable test follows a repeatable sequence:

1. Inspect the apparatus, identify hazards, and verify instrument ranges.
2. Confirm calibration or zero readings for pressure, temperature, torque, flow, and gas analysers.
3. Start the system according to the manufacturer’s procedure and allow steady operation.
4. Record data only after selected variables remain acceptably stable.
5. Change one principal operating variable, usually load or flow rate, while holding other conditions as constant as possible.
6. Repeat selected points to estimate repeatability.
7. Apply conservation equations, check units, and compare input and output energy.
8. Report uncertainty, abnormal observations, and limitations.

A measurement is meaningful only when its location and sign convention are known. For example, a temperature measured at a compressor discharge is not interchangeable with room temperature, and a gauge pressure is not an absolute pressure. The conversion is

where p_abs is absolute pressure, p_gauge is gauge pressure, and p_atm is local atmospheric pressure. Thermodynamic property relations generally require absolute pressure and absolute temperature.

For an estimated result y = f(x₁, x₂, …, x_n), a first-order combined standard uncertainty is

where u_xi is the standard uncertainty of input x_i. This expression assumes small uncertainties and approximately independent inputs. Correlation terms must be included when measurements are correlated.

Internal-Combustion Engine Testing

Principles and Measurements

An engine converts the chemical energy of fuel into shaft work, heat rejected through cooling and exhaust, and frictional losses. A typical test bench includes a dynamometer, torque measurement, speed measurement, fuel-flow device, air-flow device, cooling-water circuit, exhaust-temperature sensors, and an emissions analyser.

Brake power is obtained from torque and angular speed:

where P_b is brake power (W), N is rotational speed (rev/min), and T is brake torque (N·m). The factor 60 converts minutes to seconds. If speed is expressed in rad/s, use P_b = Tω.

Fuel energy input is

where ṁ_f is fuel mass flow rate (kg/s) and CV is the fuel lower or higher calorific value (J/kg). The selected calorific value must be stated because lower heating value and higher heating value are not identical.

Brake thermal efficiency is

and brake specific fuel consumption is

Usually, bsfc is reported in kg/(kW·h) or g/(kW·h). These measures apply to a running engine producing shaft power; they are not appropriate for comparing an engine that is motoring without combustion unless the energy accounting is redefined.

A simplified engine heat balance is

where Q̇_c is heat removed by coolant, Q̇_ex is exhaust-gas energy above a reference state, Q̇_un is unaccounted or incomplete-combustion loss, and Q̇_other includes radiation and measurement discrepancy. Coolant heat transfer is often estimated by

provided the coolant remains single-phase and its specific heat is suitably approximated as constant.

Worked Example: Engine Performance

An engine operates at 1,500 rev/min and produces 80 N·m torque. Fuel consumption is 4.0 kg/h, and the fuel lower heating value is 42 MJ/kg. The brake power is

P_b = 2π(1500)(80)/60 = 12,566 W ≈ 12.57 kW.

Fuel flow is ṁ_f = 4.0/3600 = 0.001111 kg/s. Therefore,

Q̇_f = 0.001111 × 42,000,000 = 46.67 kW.

Thus,

η_b = 12.57/46.67 = 0.269,

or approximately 26.9%. The specific fuel consumption is 0.001111/12.566 = 0.0000884 kg/(kW·s), which is 318 kg/(kW·h) after multiplying by 3,600,000 g·s/(kg·h·kW) appropriately; more directly, 4.0 kg/h ÷ 12.57 kW = 0.318 kg/(kW·h), or 318 g/(kW·h). The direct hourly calculation is the safest reporting method.

Load and Emissions

At very low load, friction and pumping work form a larger fraction of fuel input, so brake efficiency is commonly low. Efficiency generally improves with load until thermal, mechanical, combustion, or speed limitations become important. Emissions should be interpreted with operating conditions. Carbon monoxide (CO) often indicates incomplete oxidation; unburned hydrocarbons indicate incomplete combustion or fuel escape; nitrogen oxides (NOₓ) are strongly influenced by high combustion temperature and oxygen availability; particulate matter is especially important in diffusion-flame and diesel combustion.

Gas analysers require warm-up, zero/span checks, leak-free sampling, correct filtration, and attention to a dry or wet measurement basis. Emission concentration alone does not give total pollutant mass. A mass emission rate requires exhaust mass flow and concentration, with appropriate corrections for oxygen, moisture, and reference conditions.

Boiler Performance and Heat Balance

A boiler transfers heat from fuel combustion or another source to water and steam. A test normally measures fuel flow, feedwater flow, feedwater temperature, steam pressure and quality, blowdown, flue-gas temperature, and flue-gas composition.

The direct method of boiler efficiency is

where ṁ_s is steam flow rate, h_s is steam specific enthalpy, h_fw is feedwater enthalpy, and ṁ_f CV is fuel energy rate. If steam is wet, its enthalpy may be calculated from

where x is dryness fraction, h_f is saturated-liquid enthalpy, and h_fg is latent enthalpy at the measured pressure. This relation applies to a saturated liquid–vapour mixture, not to superheated steam.

The indirect method estimates losses, such as dry flue-gas loss, moisture loss, radiation, unburned fuel, and blowdown. It is useful diagnostically, but it depends heavily on accurate gas analysis and assumptions about reference temperatures.

Boiler testing requires particular care because pressure vessels store substantial energy. Never defeat safety valves, operate above rated pressure, open fittings under pressure, or introduce cold feedwater suddenly into overheated equipment. Relevant institutional procedures and pressure-vessel regulations take precedence over experimental convenience.

Compressor Testing

A compressor raises gas pressure by consuming shaft or electrical power. Measurements include inlet and delivery pressure, inlet and delivery temperature, flow rate, speed, and input power. For a steady-flow compressor neglecting changes in kinetic and potential energy,

The isentropic efficiency of a compressor is

where state 2s is the ideal isentropic discharge at the measured discharge pressure. The numerator is the minimum ideal enthalpy rise and the denominator is the actual enthalpy rise. For an ideal gas with approximately constant specific heat,

where γ = c_p/c_v. This ideal-gas expression is unsuitable when real-gas effects or large temperature-dependent property changes are significant.

Volumetric efficiency compares the actual inlet volume flow with the swept volume rate. Clearance volume, valve losses, heating of suction gas, leakage, and pressure pulsations reduce it. Compressor tests should distinguish indicated, shaft, and electrical power because motor and transmission losses may be included in measured input power.

Refrigeration and Air-Conditioning Systems

A vapour-compression plant consists principally of compressor, condenser, expansion device, and evaporator. The refrigerant absorbs heat in the evaporator and rejects heat in the condenser. For a steady cycle, neglecting kinetic and potential energy changes,

where Q̇_L is refrigeration capacity and Ẇ_in is compressor power. At the evaporator,

and compressor power is approximately

Thus, when the same refrigerant mass flow passes through the cycle,

An air-conditioning system may be evaluated by sensible, latent, and total cooling loads. For a water or air stream with negligible phase change,

with the sign selected so that cooling capacity is positive. For moist air, total enthalpy difference is preferred:

where ṁ_da is dry-air mass flow rate and h is moist-air enthalpy per unit mass of dry air.

The heat-rejection coefficient of performance is sometimes reported as

for an ideal steady refrigeration cycle in which Q̇_H = Q̇_L + Ẇ_in. COP is not a thermal efficiency and can exceed unity because it represents heat moved per unit work, not conversion of heat into work.

Worked Example: Refrigeration COP

A test rig circulates refrigerant at 0.020 kg/s. Measured enthalpies are h₁ = 398 kJ/kg, h₄ = 250 kJ/kg, and h₂ = 430 kJ/kg. Then

Q̇_L = 0.020(398−250) = 2.96 kW.

Compressor power from the refrigerant enthalpy rise is Ẇ_c = 0.020(430−398) = 0.64 kW. Therefore COP_R = 2.96/0.64 = 4.63. If electrical input including motor losses is 0.80 kW, the measured system COP is 2.96/0.80 = 3.70. The distinction demonstrates why the power boundary must be stated.

Heat-Exchanger Performance

Heat exchangers transfer energy between fluids without intentional mixing in most laboratory devices. The heat-capacity rates are

The heat-transfer rate can be calculated from either stream:

For an adiabatic exchanger with negligible losses, these values are equal. Their difference is a useful diagnostic of measurement error and environmental heat leakage.

The effectiveness is

where

and Ċ_min is the smaller heat-capacity rate. Effectiveness lies between zero and one for a physically consistent, nonreactive exchanger under the usual definition. The log-mean temperature difference is

where ∆T₁ and ∆T₂ are the terminal temperature differences appropriate to parallel or counterflow arrangement. It must not be used when the terminal differences have opposite signs without careful treatment. The heat-transfer equation is

where U is overall heat-transfer coefficient and A is heat-transfer area.

Counterflow generally achieves a larger temperature driving force than parallel flow for the same inlet conditions. Fouling, air pockets, maldistribution, low flow, and inaccurate temperature placement can reduce apparent performance.

Integrated Illustrative Case: Diagnosing a Refrigeration Test Rig

Background. An instructional vapour-compression rig is expected to provide 3.0 kW of cooling. During a student test, the measured cooling capacity is 2.4 kW and COP is substantially below the previous laboratory result.

Problem. The data show fluctuating suction pressure, a high condenser outlet temperature, and a 12% mismatch between evaporator-side and condenser-side energy balances.

Analysis. Students first verify flow-meter calibration and temperature-sensor placement. They then inspect the sight glass, condenser airflow, insulation, and refrigerant charge. The high condenser temperature suggests inadequate heat rejection, while fluctuating suction pressure may indicate unstable expansion-device operation or insufficient charge. The energy mismatch is too large to dismiss as rounding.

Approach. The rig is stopped safely. The condenser fan filter is cleaned, airflow is restored, and the pressure transducers are checked against a reference gauge. A leak test and manufacturer-approved charge verification are performed by competent personnel. The test is repeated only after steady state is reached. Refrigerant enthalpies are obtained at measured pressures and temperatures from a consistent property source.

Outcome. The repeated test gives 2.9 kW cooling, 0.78 kW electrical input, and COP = 3.72. The two heat-rate estimates differ by 3%, which is acceptable for the stated instrument uncertainties. The result demonstrates that performance deterioration may arise from heat-transfer fouling, instrumentation error, or operating instability—not necessarily from compressor failure.

Learning points. A valid laboratory conclusion requires a defined system boundary, repeatable steady-state data, independent balance checks, and diagnosis based on several measurements rather than one abnormal reading.

Data Interpretation, Safety, and Professional Practice

Performance curves should show the independent variable and operating conditions clearly. Examples include brake power versus speed, efficiency versus load, compressor efficiency versus pressure ratio, COP versus evaporating temperature, and exchanger effectiveness versus flow-rate ratio. Do not connect sparse data with a smooth curve unless the interpolation is justified.

Common errors include mixing kPa and Pa, using gauge pressure in property tables, confusing mass and volume flow, applying constant c_p over a large temperature range, ignoring motor power, and reporting excessive significant figures. A heat balance that differs by 20% should trigger investigation, not forced adjustment.

Safety hazards include rotating shafts, hot surfaces, steam pressure, combustion gases, electrical power, refrigerant pressure, and oxygen-deficient or toxic atmospheres. Guards must remain installed; emergency stops must be known; exhaust must be extracted; pressure systems must be inspected; and refrigerants must be handled according to applicable environmental and occupational regulations. Never vent refrigerant or combustion products deliberately.

Digital acquisition, automated dashboards, and machine-learning models can identify drift, detect sensor disagreement, or predict fouling. However, AI does not replace calibration, conservation laws, or engineering judgement. Training data must represent the operating range, anomalous readings must remain visible, and any automated decision affecting safety must be independently verified.

A professional report should contain apparatus and operating conditions, calibration information, raw data, sample calculations, property sources, uncertainty estimates, plots, heat balances, deviations from expected behaviour, safety observations, and conclusions tied directly to evidence.

Chapter Summary

Thermal-system testing is an application of conservation of mass and energy supported by careful measurement. Engine tests use torque, speed, fuel flow, thermal efficiency, specific fuel consumption, heat balances, and emissions. Boiler tests determine useful steam output and losses while respecting pressure-vessel safety. Compressor tests distinguish actual from isentropic work and account for pressure ratio and volumetric effects. Refrigeration and air-conditioning tests use cooling capacity, enthalpy differences, and COP, while heat-exchanger tests use heat-capacity rates, effectiveness, LMTD, and overall conductance. Across all systems, reliable conclusions require steady operation, calibrated instruments, consistent boundaries, unit discipline, uncertainty analysis, and independent balance checks.

Key Terms

Brake power: Shaft power delivered by an engine.

Calorific value: Energy released per unit mass of fuel during complete combustion.

Coefficient of performance: Useful heating or cooling rate divided by work input.

Control volume: A selected region through which mass and energy may flow.

COP_R: Refrigeration coefficient of performance.

Dryness fraction: Mass fraction of vapour in a saturated liquid–vapour mixture.

Effectiveness: Actual heat transfer divided by maximum possible heat transfer.

Enthalpy: A thermodynamic property defined as internal energy plus pressure–volume energy.

Heat balance: Accounting of energy entering, leaving, and accumulating in a system.

Isentropic efficiency: Ratio comparing ideal reversible compression or expansion with actual performance.

LMTD: Log-mean temperature difference used in heat-exchanger analysis.

Lower heating value: Fuel energy excluding latent heat recovered by condensing combustion water vapour.

Mass flow rate: Mass passing a section per unit time.

Overall heat-transfer coefficient: Combined measure of conductive and convective thermal resistance.

Performance map: Graphical relation between performance and operating variables.

Specific fuel consumption: Fuel mass consumed per unit brake power and time.

Steady state: Condition in which selected system properties do not vary significantly with time.

Uncertainty: Quantified doubt associated with a measured or calculated result.

Volumetric efficiency: Actual intake volume relative to the theoretical swept-volume intake.

Review Questions

Short Answer Questions

1. Why must absolute pressure be used in many thermodynamic property relations?
2. Define brake thermal efficiency and state its principal measurements.
3. What is the physical meaning of refrigeration COP?
4. Why are the two heat-transfer rates in a heat exchanger ideally equal?
5. Identify two important safety hazards in boiler testing.

Long Answer Questions

1. Describe a complete experimental procedure for testing an internal-combustion engine from startup to reporting.
2. Explain the direct and indirect methods of determining boiler efficiency, including their strengths and limitations.
3. Derive the expression for refrigeration COP in terms of refrigerant enthalpies.
4. Explain isentropic compressor efficiency and discuss the influence of pressure ratio and clearance volume.
5. Compare parallel-flow and counterflow heat exchangers using temperature driving force and effectiveness.

Analytical / Application Questions

1. An engine produces 60 N·m at 1,800 rev/min and consumes 3.2 kg/h of fuel with a calorific value of 43 MJ/kg. Calculate brake power, fuel energy rate, brake thermal efficiency, and specific fuel consumption.
2. A heat exchanger has hot-stream capacity rate 1.5 kW/K and cold-stream capacity rate 1.0 kW/K. The inlet temperatures are 120°C and 25°C, and the actual heat transfer is 62 kW. Calculate the maximum possible heat transfer and effectiveness.
3. During a refrigeration test, the evaporator-side and condenser-side heat rates differ by 15%. Propose a systematic diagnostic plan, identifying at least four possible causes and the measurements needed to distinguish them.

Multiple Choice Questions with Answers

Question 1

An engine operates at 1,500 rev/min with a torque of 80 N·m. What is its brake power?

A. 6.28 kW

B. 12.57 kW

C. 18.85 kW

D. 25.13 kW

Correct Answer: B. 12.57 kW

Question 2

Which expression represents brake thermal efficiency?

A. Fuel flow rate divided by brake power

B. Brake power divided by fuel energy input rate

C. Cooling-water heat divided by fuel flow rate

D. Exhaust temperature divided by inlet temperature

Correct Answer: B. Brake power divided by fuel energy input rate

Question 3

A refrigeration system provides 3 kW of cooling with 0.75 kW compressor input. Its refrigeration COP is:

A. 0.25

B. 2.25

C. 4.00

D. 3.75

Correct Answer: C. 4.00

Question 4

For a saturated liquid–vapour mixture, dryness fraction represents the:

A. Ratio of liquid volume to total volume

B. Mass fraction of vapour

C. Ratio of vapour pressure to atmospheric pressure

D. Mass flow rate of condensate

Correct Answer: B. Mass fraction of vapour

Question 5

In compressor isentropic efficiency, the numerator is the:

A. Actual enthalpy rise

B. Ideal isentropic enthalpy rise

C. Electrical motor loss

D. Suction-side pressure drop

Correct Answer: B. Ideal isentropic enthalpy rise

Question 6

The maximum possible heat transfer in a heat exchanger is calculated using:

A. The larger heat-capacity rate and outlet temperatures

B. The smaller heat-capacity rate and inlet temperature difference

C. Only the hot-stream outlet temperature

D. The logarithm of the pressure ratio

Correct Answer: B. The smaller heat-capacity rate and inlet temperature difference

Question 7

Why can refrigeration COP be greater than one?

A. It is a percentage efficiency of combustion

B. It measures heat moved per unit work rather than heat converted to work

C. The compressor creates energy

D. The condenser rejects no heat

Correct Answer: B. It measures heat moved per unit work rather than heat converted to work

Question 8

Which emission is commonly associated with incomplete combustion?

A. Carbon monoxide

B. Oxygen only

C. Nitrogen

D. Water vapour only

Correct Answer: A. Carbon monoxide

Question 9

If a pressure sensor reads 300 kPa gauge and atmospheric pressure is 100 kPa, the absolute pressure is:

A. 200 kPa

B. 300 kPa

C. 400 kPa

D. 30 kPa

Correct Answer: C. 400 kPa

Question 10

A heat exchanger transfers 40 kW while its maximum possible transfer is 80 kW. Its effectiveness is:

A. 0.25

B. 0.50

C. 1.50

D. 2.00

Correct Answer: B. 0.50